Đáp án:
$\begin{array}{l}
21)x\left( {{x^2} - x - 2} \right) - \left( {x + 5} \right)\left( {x - 1} \right)\\
= {x^3} - {x^2} - 2x - \left( {{x^2} + 4x - 5} \right)\\
= {x^3} - 2{x^2} - 6x + 5\\
22)\\
\left( {x + 5} \right)\left( {x - 7} \right) - \left( {x - 4} \right)\left( {x + 3} \right)\\
= {x^2} - 2x - 35 - \left( {{x^2} - x - 12} \right)\\
= - x - 23\\
23)\left( {x - 1} \right)\left( {x + 2} \right) - \left( {x + 5} \right)\left( {x - 2} \right)\\
= {x^2} + x - 2 - \left( {{x^2} + 3x - 10} \right)\\
= - 2x + 8\\
24)\left( {2x - 3} \right)\left( {x + 4} \right) + \left( { - x + 1} \right)\left( {x - 2} \right)\\
= 2{x^2} + 5x - 12 - {x^2} + 3x - 2\\
= {x^2} + 8x - 14\\
25)\left( { - x + 5} \right)\left( {x + 3} \right) + \left( {2x - 1} \right)\left( {x + 3} \right)\\
= - {x^2} + 2x + 15 + 2{x^2} + 5x - 3\\
= {x^2} + 7x + 12\\
26)\left( {x + 2} \right)\left( {x - 1} \right) - \left( {x - 7} \right)\left( {x - 6} \right)\\
= {x^2} + x - 2 - \left( {{x^2} - 13x + 42} \right)\\
= 14x - 44\\
27)\left( { - x - 2} \right)\left( {x + 1} \right) - \left( {x - 5} \right)\left( { - x + 1} \right)\\
= - {x^2} - 3x - 2 - \left( { - {x^2} + 6x - 5} \right)\\
= - 9x + 3\\
28)5x\left( {x - 3} \right)\left( {x - 1} \right) - 4x\left( {{x^2} - 2x} \right)\\
= 5x\left( {{x^2} - 4x + 3} \right) - 4{x^3} + 8{x^2}\\
= 5{x^3} - 20{x^2} + 15x - 4{x^3} + 8{x^2}\\
= {x^3} - 12{x^2} + 15x\\
29) - 4x\left( {x + 3} \right)\left( {x - 4} \right) - 3x\left( {{x^2} - x + 1} \right)\\
= - 4x\left( {{x^2} - x - 12} \right) - 3{x^3} + 3{x^2} - 3x\\
= - 4{x^3} + 4{x^2} + 48x - 3{x^3} + 3{x^2} - 3x\\
= - 7{x^2} + 7{x^2} + 45x\\
30) - 3\left( {x + 4} \right)\left( {x - 7} \right) + 7\left( {x - 5} \right)\left( {x - 1} \right)\\
= - 3\left( {{x^2} - 3x - 28} \right) + 7\left( {{x^2} - 6x + 5} \right)\\
= - 4{x^2} + 9x + 84 + 7{x^2} - 42x + 35\\
= 3{x^2} - 33x + 119\\
31)4x\left( {{x^2} - x + 3} \right) - \left( {x - 6} \right)\left( {x - 5} \right)\\
= 4{x^3} - 4{x^2} + 12x - {x^2} + 11x - 30\\
= 4{x^3} - 5{x^2} + 23x - 30
\end{array}$
